Instrumental variable methods are widely used for causal inference, but identification becomes especially challenging when instruments are weak and potentially invalid. These challenges are particularly pronounced in Mendelian randomization, where genetic variants serve as instruments and violations of exclusion restriction or independence assumptions are common. We propose MAGIC, a constructive and assumption-lean framework that achieves identification even when all candidate instruments may be invalid. The method exploits pairwise and higher-order interactions among mutually independent instruments to construct moment conditions orthogonal to both unmeasured confounding and direct effects under a linear structural model. The resulting estimation problem involves many potentially weak interaction moments with unknown nuisance parameters. We develop a semiparametric generalized method of moments estimator and introduce a global Neyman orthogonality condition to ensure robustness of both the moment function and its derivative to nuisance estimation under many weak moment asymptotics. We establish consistency and asymptotic normality when the number of moments diverges with sample size and characterize the semiparametric efficiency bound under fixed dimension. Simulations and an application to UK Biobank data illustrate the method.

翻译：工具变量方法广泛应用于因果推断，但当工具变量较弱且可能存在无效性时，识别问题变得尤为困难。这些挑战在孟德尔随机化研究中尤为突出——该场景下遗传变异作为工具变量，且排除限制或独立性假设的违背现象十分普遍。我们提出MAGIC框架，这是一种构造性且假设精简的识别框架，即使在所有候选工具变量都可能无效的情况下仍能实现识别。该方法利用相互独立工具变量间的配对及高阶交互作用，在线性结构模型下构建与未观测混杂因子及直接效应均正交的矩条件。由此产生的估计问题涉及大量可能较弱的交互矩，且其中包含未知 nuisance 参数。我们开发了半参数广义矩估计方法，并引入全局奈曼正交条件，以确保在众多弱矩渐近框架下，矩函数及其导数均对 nuisance 参数估计具有稳健性。当矩数量随样本量发散时，我们建立了估计量的一致性和渐近正态性，并在固定维度情形下刻画了半参数效率界。通过数值模拟和英国生物样本库数据应用验证了该方法的有效性。